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MATH 3070 Introduction to Probability and Statistics
Lecture notes
Measures of Position
Objectives:
1. Understand and use the Empirical Rule
The Empirical Rule (68-95-99.7)
If the distribution of the data is approximately symmetrical with a single peak we
usually refer to this as a normal distribution. The distribution is centered around
the mean and has noticeable changes in slope at various points related to the standard
deviation. We can say this about the data:
1. 68% of the observations fall within 1 standard deviation of the mean.
2. 95% of the observations fall within 2 standard deviations of the mean.
3. 99.7% of the observations fall within 3 standard deviations of the mean.
How can we know this? It depends upon the curve and the characteristics of a
symmetrical curve, or density curve. The area underneath the curve is 1 and always
positive. The curve bends at each multiple of the standard deviation. These bending
points are called inflection points.